Visual aid for arithmetic computation



May 27, 1958 H. HILKENE 2,835,988

VISUAL AID FOR ARITHMETIC coMPuTATIoN Filed Dec. 2o. 1955 ,e2 vf -20 INVENTQR.

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United States Patent 2,835,988y Patented May 27, 1958 ice This invention relates to an educational device for use as a visual aid in the teaching of certain arithmetical computations.

In the teaching of children, especially in the eld of arithmetic or number computation, it has been found that use of visual aids is of advantage, especially to help in memorizing products of number calculations. Various devices are known by which a rudimentary arithmetic process such as addition of numbers can be visualized, but it does not appear that a simple, compact and easily manipulatable device has been available by which a more complex arithmetic process such as multiplication of one number by another can be quickly carried out and the resultant product immediately visibly indicated merely by manipulation of multiplicand and multiplier denoting pieces.

It is therefore an object of this invention to provide a simple device by which the arithmetic process of multiplication can be visually aided; said device comprising at least two sets of blocks or pieces, the blocks or pieces of each set respectively denoting different numerical values, e. g. from 2 to l() inclusive, and being of diierent lengths proportional to the logarithms of the numbers denoted thereby, and a holder to which selected blocks or pieces, respectively denoting numbers desired to be multiplied one by the other, can be applied in end to end relation for reference to a product number indicating scale borne by the holder; the product number indicating graduationsof said scale being relatively spaced proportionately to the logarithms of the product numbers indicated thereby, said product numbers being includedwithin a range e. g. from 2 to l0@ inclusive, 1 being a zero or base indication relative to which the applied number blocks or pieces are based their operative end to end assembled relation with the holder.

The above stated other objects will be understood from a reading of the following7 detailed description of this invention in connection with the accompanying draw ings, in which: A

Fig. l is a top plan View of a holder to which number denoting blocks or pieces can be removably applied; and Fig. 2 is a vertical cross-sectional view, taken on line 2-2 in Fig. l.

Figs. 3 and 4, taken together, present face views of sets of number denoting blocks or pieces, selections from which are adapted to be applied to the holder of Fig. 1.

Fig. 5 is a perspective view of one of the blocks or pieces from a set thereof.

As shown in Figs. 3 and 4, at least two sets of number denoting blocks or pieces are provided, each set thereof comprising nine blocks or pieces of like width and thickness but of various lengths, and respectively bearing numbers 2 to 10 inclusive. In use, said two sets of blocks or pieces, together totaling eighteen blocks or pieces, are all that are necessary to carry out multiplication of numbers in the range of 2X2 to 10X l0 inclusive.

The respective lengths of individual blocks or pieces of each set thereof are calculated with reference to logarithms to the base ten, whereby the logarithms of the numbers borne by the respective blocks or pieces determine respective lengths thereof, in accordance with the following logarithm table laid out with referencevto an inch unit of linear measurement, wherein:

1= 0. inch 2: 3.0103 inches 3= 4.7712 inches 4= 6.0206 inches 5= 6.9897 inches 6= 7.7815 inches 7= 8.4510 inches 8= 9.0309 inches 9: 9.5424 inches 10:10.0000 inches From the above table, it will be obvious that the relative lengths of the blocks or pieces are not based on multiples of the unit or linear measurement, and conse# quently do not follow a uniform progressive pattern with respect to relative lengths thereof', but rather a pattern whereby their relative lengths vary in proportion to the logarithmic differences of the numbers borne thereby.

Although, Yfor purposes of iiiustration, the above logarithm table is laid out with reference to the inch as a unit of linear measurement, it can optionally be laid out with reference to any other suitable unit or" linear i easurement.

The device of this invention further includes a holder to which selected blocks or pieces from the sets thereof Y can be applied to ascertain and Visualize the product resulting from multiplication of the numbers borne by the applied blocks one by the other. An illustrative form of the holder, as shown, comprises an elongated body 20 provided with an outwardly open longitudinal nnoel Zi, closed at its bottom end by an end wall 22. The width and depth of said channel El correspond respectively to the widths and thicknesses of the blocks or pieces to be applied thereto. 0n the marginal faces of the body Ztl of the holder, which border opposite longitudinal sides of the block or piece receiving channel El thereof, are inscribed scales graduated to indicate Various product numbers, e. g. within a range of 2 to 100 inclusive, which result from multiplication one by the other of numbers borne by blocks or pieces operatively applied to the holder. One scale is provided with a graduation marked l which is disposed in aligned registration with the inner face or the end wall 22 Of the holder, thus providing a zero or base indication relative to which the applied blocks or pieces are footed when operatively arranged in end to end relation in the receiving channel 2l of the holder. As shown, the product number indicating scale is arranged in two sections respectively inscribed on the respective faces of the holder body 20 which border the receiving channel 21. This is a preferred but not an essential arrangement, since the scale could be arranged as a single continuous scale entirely on one side of the receiving channel 21. The two section arrangement shown is preferred however since it permits wider separation of those graduations and their associated product indicating numbers, which otherwise would be brought into close adjacency. The wider separation of such graduations makes for easier reading of the scale. The graduations of the scale are relatively spaced proportionally to the logarithmic dilferences of the product numbers indicated thereby.

in the use and manipulation of the device, blocks or pieces respectively bearing numbers desired to be multi- Y plied one by the other are deposited within the receiving channel 21 of the holder 2i) in end to end relation, with the lower block or piece footed upon the end wall 22 so that its bottom end is in register with the zero or base mark l of the product indicating scale. When the applied blocks or pieces are thus arranged the top end of upper block or piece will register with that product number indicating graduation of the scale which gives the product which would be obtained by multiplication auf .the numbers of the applied blocks or piecescne by multiplier figure.

,of one numberrlby another. i Y it; is desired to divide 8 by 4, the blocks or pieces bearing Q V l2,835,938 Y* Y Y' fl the other. By way of example, assume it is desired to ,multiply 2X4. A block orrpiece bearing number 2 is footed in therreeeiving channel 21 of the holder 20, and then a block or vpiece bearing number 4 is entered `in said receiving channel in end toend abutting relation to the entered block or piece bearing the number 2 '(see broken line showing oi such blocks or pieces in Fig. 1). Byrsuch end to end disposition of said blocks or pieces, the top end of the upper block or piece is registered in alignment with the graduationof the scale which indicates ythe product numberV Sy thus immediately visually disn multiplication process Vand product indication is directly and immediately obtained, without necessity for selecting,

independently manipulating, and comparing product v indicatingcomparison blocks or pieces in addition to the multiplicand and multiplier blocks, or without necessity for using a plurality of multiplicand indicating Vblocks or pieces, fthe number thereof so Vused denoting the The device of this invention can also be used to visually demonstrate more complex problems of multiplication,

such asrthe multiplication of the product of two members by a third member; for example, 2 4 5. rlf`he product of 2 4Vhaving been demonstrated to be 8 in the manner above described, assume that it isrdesired to `multiply such product by Va thirdrnumbrer, for example 5. In

' such case, all that is necessary to be done isV to enter in theV receiving channel 2l of the holder body 20 ablock or piece numbered 5 in end to endY relation to VAvisaually demonstrating the problem 2 4 5=740- Although the device of this invention is especially well Y :adapted to visually demonstrate the arithmetic process of multiplication of numbers, it mayV alsorbe used to visually demonstrateV thearithmretic process of'division ForV example, assumeY that f consecutive numbers 2 to 10 inclusive, each rpiece having a length which is determined with reference-to a selected, unit of linear measurement by the logarithms to the basej p W ten of thcpnumber borne thereby, and a holder comprisingV ing consecutive numbers beginning with 2 on thecshortest piecesaid pieces being of'various lengths, a holder comprising an elongated body having an outwardly open longitudinally extending channel therein closed at one endV by an end wall, said channel being adapted'to receive selected pieces disposed in end to'end relation to abut and extendV fromrthe endfwall'thereof, and marginal portions of the Y top face'of the holder body bordering `the piece receiving Y channel thereof havingia graduated scale thereon, the

graduations of which are respectively denoted byrnumbers. within the range of 1 to 100 or more, with thetnumber 1j graduation aligned with the piece engageableinner face y of theV endwall of said receiving channel, the Ylengths of j respective pieces of each set thereof and the spacing of, Y

Vnumbers borne by saidpieces and the logarithms of the i numbers denoting said graduations.'V Y' 2. A device of the kinddescribedcomprising at leastV two sets of pieces, each set thereof comprising nine; pieces of progressively increased length and respectively bearing an elongated body having means to receive selected pieces in end to end relation and an abutment in' engagement with which the received pieces are footed, Vsaid holder body having a graduated scale bordering the receiving means thereof to which the received pieces are adapted to refer;y i the graduations of said scale being denoted by numbers il to 100, with the number l'rgrad'uation aligned t'vith'theV t ment as used to determinejthe lengthsof the pecesrbutfin the respectively numbered Vblocks or pieces 2 and 4 t 'Y previously mounted in the holder, whereupon the top Vend Yof the added block or piece 5 will register in align- Y the numbers 2 and '4 are entered in the receivingV channel t Y' 2,1 of theV holder body 2li (astshown by'broken lines in ,Figl 1), so that the 4Vblocl or piece (the divisor) registers` withV the scale graduation marked: 8Y (the dividend). This Yhaving been done, ther4 blockY or piece is removed, whereupon the tcp end ofthe ramaining block or piece Vregisters with the scale graduation marked 2,"which Vgives the,y quotinent, and thus visually demonstrates 'the prob-V With respect to the holdenalthough, the channeled having'an area'to' receive the pieces, to which Varea theV scale'gaduations VYare parallel.Y I t will also'be understood` that the pieces Vdo not haveto vbe orl block form, but

may merelyV comprise a'tvpieces'ge, g. cardboard of suitable width and of lengths determined as Vabove described with reference to the blocks.V lnA fact any suitablefconstruction of holderte'which the pieces can be applied Vaccordance with the logarithrns tothe base ten of the*Y Y t numbers denoting said graduations. v Y V 3.V device of the kindrdescribed comprising 'Vat' yleastV two sets of elongate pieces of suitable width and thickness,

each set comprising nine pieces'ofprogressively increasedV length and respectively bearing numbers'Z'to lO'inclusiverV each piece having a lengthtvrihirch is Vdetermined'with referi t Vence to` a selectedttunit of Vlinear measurement? byY the`V logarithms to the base ten ofthefnurnberboruetherebjgk Yand a holder comprising an'elon'gatedV bodyrhavinglanV outwardly open longitudinally extending channel'thereinV (closed at one end by an end wa]l,"said Vchannel ,lzfe'ingrY adapted ,to receive selected pieces disposed in end toend relation to abut and'extend from the end Vwall thereohsaid Y n channel being of widthV and depth corresponding to the width and thickness of the pieces, marginalportionsof the top face of the holder body bordering( opposite sides e ofthe piece receiving'channel thereof having complementary sectionsV of a graduated scale, the combined 'gradua-k tionslof which are successively denoted by numbersi 1 to end Vto Vend in such position as to cooperatewith product t indicating scale mayprovided. A Havingnow described umy invention, lfclaim;Y Y f 1. A device of the kind described comprising Vati-least YYtwo sets of pieces, the pieces of each set respectively hear,`

100, withthe'numberrl graduation aligned'with the. piece' engageable innerlfaceiof the end wall of the receiving Y channel, the'graduationsV of said scale beingcalibrated with reference tothe same unit of linear rneasuremientrasV Y used to determine'the lengthsof the pieces but iniaccordance with the logarithms tothe base tenjof Vthenumber's denoting said graduations. f t 1 References Cited inthe tile of this patent Y, UNITED sTAras PATENTS 

